Texture on box stretching on the vertical axis
Basically, the Generated coordinates take the object to have equal size along all three axes, and textures get mapped to between 0 and 1, which can cause stretching or deflating.
The Object coordinates take into consideration the object's actual size, and map textures according to that.

With this texture



I get this with Generated



this with Object and Extension set to Repeat



and this with Object and Extension set to Clip



With Generated in this case Clip or Repeat doesn't make a difference, since the image gets stretched across the entire surface either way.
The above examples I believe are the most relevant to your specific case, but for more in-depth explanations of texture coordinates, this post by PGmath is definitely good reading. Also Manipulate texture coordinates like a boss is an excellent lecture by Bartek Skorupa. Mr. Skorupa focuses mainly on Cycles, but the underlying coordinates work the same in Internal, so you shouldn't have a problem with it if you want to stick to Internal.